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function info = perfect_foresight_simulation(compute_linear_solution,steady_state)
% Performs deterministic simulations with lead or lag on one period
%
% INPUTS
% endo_simul [double] n*T matrix, where n is the number of endogenous variables.
% exo_simul [double] q*T matrix, where q is the number of shocks.
% compute_linear_solution [integer] scalar equal to zero or one.
%
% OUTPUTS
% none
%
% ALGORITHM
% Laffargue, Boucekkine, Juillard (LBJ)
% see Juillard (1996) Dynare: A program for the resolution and
% simulation of dynamic models with forward variables through the use
% of a relaxation algorithm. CEPREMAP. Couverture Orange. 9602.
%
% SPECIAL REQUIREMENTS
% None.
% Copyright (C) 2009-2015 Dynare Team
%
% This file is part of Dynare.
%
% Dynare is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% Dynare is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
global M_ options_ it_ oo_
persistent lead_lag_incidence dynamic_model ny nyp nyf nrs nrc iyf iyp isp is isf isf1 iz icf ghx iflag
if ~nargin && isempty(iflag)% Initialization of the persistent variables.
lead_lag_incidence = M_.lead_lag_incidence;
dynamic_model = [M_.fname '.dynamic'];
ny = size(oo_.endo_simul,1);
nyp = nnz(lead_lag_incidence(1,:));% number of lagged variables.
nyf = nnz(lead_lag_incidence(3,:));% number of leaded variables.
nrs = ny+nyp+nyf+1;
nrc = nyf+1;
iyf = find(lead_lag_incidence(3,:)>0);% indices for leaded variables.
iyp = find(lead_lag_incidence(1,:)>0);% indices for lagged variables.
isp = 1:nyp;
is = (nyp+1):(nyp+ny); % Indices for contemporaneaous variables.
isf = iyf+nyp;
isf1 = (nyp+ny+1):(nyf+nyp+ny+1);
iz = 1:(ny+nyp+nyf);
icf = 1:size(iyf,2);
info = [];
iflag = 1;
return
end
initial_endo_simul = oo_.endo_simul;
warning_old_state = warning;
warning off all
if nargin<1
compute_linear_solution = 0;
else
if nargin<2
error('The steady state (second input argument) is missing!');
end
end
if ~isstruct(compute_linear_solution) && compute_linear_solution
[dr,info,M_,options_,oo_] = resol(0,M_,options_,oo_);
elseif isstruct(compute_linear_solution)
dr = compute_linear_solution;
compute_linear_solution = 1;
end
if compute_linear_solution
ghx(dr.order_var,:) = dr.ghx;
ghx = ghx(iyf,:);
end
periods = options_.periods;
stop = 0 ;
it_init = M_.maximum_lag+1;
info.convergence = 1;
info.time = 0;
info.error = 0;
info.iterations.time = zeros(options_.simul.maxit,1);
info.iterations.error = info.iterations.time;
last_line = options_.simul.maxit;
error_growth = 0;
h1 = clock;
for iter = 1:options_.simul.maxit
h2 = clock;
if options_.terminal_condition
c = zeros(ny*(periods+1),nrc);
else
c = zeros(ny*periods,nrc);
end
it_ = it_init;
z = [ oo_.endo_simul(iyp,it_-1) ; oo_.endo_simul(:,it_) ; oo_.endo_simul(iyf,it_+1) ];
[d1,jacobian] = feval(dynamic_model,z,oo_.exo_simul, M_.params, it_);
jacobian = [jacobian(:,iz) , -d1];
ic = 1:ny;
icp = iyp;
c(ic,:) = jacobian(:,is)\jacobian(:,isf1) ;
for it_ = it_init+(1:periods-1-(options_.terminal_condition==2))
z = [ oo_.endo_simul(iyp,it_-1) ; oo_.endo_simul(:,it_) ; oo_.endo_simul(iyf,it_+1)];
[d1,jacobian] = feval(dynamic_model,z,oo_.exo_simul, M_.params, it_);
jacobian = [jacobian(:,iz) , -d1];
jacobian(:,[isf nrs]) = jacobian(:,[isf nrs])-jacobian(:,isp)*c(icp,:);
ic = ic + ny;
icp = icp + ny;
c(ic,:) = jacobian(:,is)\jacobian(:,isf1);
end
if options_.terminal_condition
if options_.terminal_condition==1% Terminal condition is Y_{T} = Y_{T+1}
s = eye(ny);
s(:,isf) = s(:,isf)+c(ic,1:nyf);
ic = ic + ny;
c(ic,nrc) = s\c(ic,nrc);
else% Terminal condition is Y_{T+1}-Y^{\star} = TransitionMatrix*(Y_{T}-Y^{\star})
it_ = it_+1;
z = [ oo_.endo_simul(iyp,it_-1) ; oo_.endo_simul(:,it_) ; oo_.endo_simul(iyf,it_+1) ] ;
[d1,jacobian] = feval(dynamic_model,z,oo_.exo_simul, M_.params, it_);
jacobian = [jacobian(:,iz) -d1];
jacobian(:,[isf nrs]) = jacobian(:,[isf nrs])-jacobian(:,isp)*c(icp,:) ;
ic = ic + ny;
icp = icp + ny;
s = jacobian(:,is);
s(:,iyp) = s(:,iyp)+jacobian(:,isf)*ghx;
c (ic,:) = s\jacobian(:,isf1);
end
c = bksup0(c,ny,nrc,iyf,icf,periods);
c = reshape(c,ny,periods+1);
oo_.endo_simul(:,it_init+(0:periods)) = oo_.endo_simul(:,it_init+(0:periods))+options_.slowc*c;
else% Terminal condition is Y_{T}=Y^{\star}
c = bksup0(c,ny,nrc,iyf,icf,periods);
c = reshape(c,ny,periods);
oo_.endo_simul(:,it_init+(0:periods-1)) = oo_.endo_simul(:,it_init+(0:periods-1))+options_.slowc*c;
end
err = max(max(abs(c)));
info.iterations.time(iter) = etime(clock,h2);
info.iterations.error(iter) = err;
if iter>1
error_growth = error_growth + (info.iterations.error(iter)>info.iterations.error(iter-1));
end
if isnan(err) || error_growth>3
last_line = iter;
break
end
if err < options_.dynatol.f
stop = 1;
info.time = etime(clock,h1);
info.error = err;
info.iterations.time = info.iterations.time(1:iter);
info.iterations.error = info.iterations.error(1:iter);
break
end
end
if stop && options_.terminal_condition==2
% Compute the distance to the deterministic steady state (for the subset of endogenous variables with a non zero
% steady state) at the last perdiod.
idx = find(abs(oo_.steady_state)>0);
distance_to_steady_state = abs(((oo_.endo_simul(idx,end)-oo_.steady_state(idx))./oo_.steady_state(idx)))*100;
disp(['(max) Distance to steady state at the end is (in percentage):' num2str(max(distance_to_steady_state))])
end
if ~stop
info.time = etime(clock,h1);
info.error = err;
info.convergence = 0;
info.iterations.time = info.iterations.time(1:last_line);
info.iterations.error = info.iterations.error(1:last_line);
oo_.endo_simul = initial_endo_simul;
end
warning(warning_old_state);
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